I have two GTX 760 4GB FTW cards and an Acer B286HK monitor. I can run 3840x2160 with 60 Hz refresh and there is no problem. However, to push this many pixels down the wire to the monitor, you *must* use the DisplayPort connections direct. The other signalling standards just don't have the bandwidth.
 
That said, I find that 4k in the Windows desktop does not work too great since the icons get too tiny. Yes, I could adjust the size of elements on the desktop by sizing things to 125% or more, but not everything scales neatly and it can look trashy. Also, I run a multi-monitor setup and the other monitors are not 4k so things, get out of whack quickly. If play a game that works best in single monitor mode, I'll punch it up to 4k then.
 
Running the Acer at 1080p most of the time gives a nice result.
 
 
I ran Valley Benchmark and manually set the resolution to 3840x2160. Quality was at ultra, but I did turn off anti-aliasing.
FPS:31.4
Score:1312
Min FPS:15.3
Max FPS:57.9

System

Platform:Windows 7 (build 7601, Service Pack 1) 64bit
CPU model:Intel(R) Core(TM) i7-5930K CPU @ 3.50GHz (3491MHz) x6
GPU model:NVIDIA GeForce GTX 760 9.18.13.4788 (4095MB) x2

Settings

Render:Direct3D11
Mode:3840x2160 fullscreen
PresetCustom
QualityUltra
 
By way of comparison, here is my rig running Valley Benchmark with the preset "Extreme HD" settings.
FPS:64.0
Score:2678
Min FPS:21.3
Max FPS:119.5

System

Platform:Windows 7 (build 7601, Service Pack 1) 64bit
CPU model:Intel(R) Core(TM) i7-5930K CPU @ 3.50GHz (3491MHz) x6
GPU model:NVIDIA GeForce GTX 760 9.18.13.4788 (4095MB) x2

Settings

Render:Direct3D11
Mode:1920x1080 8xAA fullscreen
PresetExtreme HD
 
In the end, what you can do will boil down to the old trade-off of quality vs. frame rate and what  works best in different circumstances.